Parameter Identification of a Chaotic Circuit with a Hidden Attractor Using Krill Herd Optimization

Abstract

Parameter estimation plays an important role in modeling and system identification. However, parameter estimation of chaotic systems has some basic differences with other dynamical systems due to butterfly effect. In this paper, we apply a new cost function for parameter estimation in a very interesting chaotic system, a system with a plane of equilibrium which belongs to a newly introduced category of dynamical systems: systems with hidden attractor. The nonlinear dynamics of this system is described in terms of equilibria and its stability, phase portraits, bifurcation diagram and Lyapunov exponents. In order to minimize the proposed cost function and obtain the correct parameters, we use a new efficient optimization method, Krill Herd algorithm. The results show the success of proposed procedures.